Download division of liberal arts and human services

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College of Science,
Te c h n o l o g y a n d A p p l ie d A r t s
O f Tr i n id a d a n d To ba g o
DIVISION OF LIBERAL ARTS AND HUMAN SERVICES
Department of Mathematics
Course Syllabus and Outline
Fundamentals of Statistics (STAT 120)
Lecturer Name:
E-mail:
Course Web Site:
Class Hours per week: 3
Number of Credits: 3
Campus Location: City Campus (Full Time and Part Time)
Material Required for Class: Course text book, Class notes, and Extra material
necessary for course content given as hand-outs.
Text Book: Statistical Reasoning for everyday Life by Jeffrey Bennett, William Briggs
and Mario Triola
Pre-requisites: In order to register in this course, students must have successfully
completed Contemporary College Mathematics (Math 116) or College Algebra,
(Math 117).
Purpose of Course: To introduce students to the fundamental concepts of
statistics and the associated mathematical principles that form the basis of the
discipline.
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Course Overall Objectives:
To give students both a conceptual understanding of the basic statistical
procedures and processes, and exposure to the mathematical principles that
underlie them.

To help students develop the skills needed to gather, sample and
draw inferences from the collected statistical data.

To help students develop analytical and problem solving skills.

To help students develop facility and skills needed for collaborative
team work.

To help students see and experience statistics and mathematics at
work in the real world using real world problems.

To lay the foundations for more advanced studies in statistics and
mathematical statistics.

To help students develop facility in the analysis of data with
computer technology using spreadsheets applications like Excel,
databases and/or dedicated statistics applications like SPSS

To stimulate interest in statistics and in mathematics in general.

To help students develop and practice skills in communicating
abstract ideas through written and oral presentation.
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Specific Course Objectives:
After completing the course, students will be able to

organize, summarize and display data in a meaningful way

identify the basic sampling techniques and solve problems using
these techniques.

simulate the circumstances of an experiment to learn how the
results would occur in reality

compute various measures of center, variability and position of
data sets

organize descriptive data by using frequency distributions and
ogive curves

apply basic rules of probability to calculate likelihoods of random
events

define and use in context the concept of a probability distribution

construct a probability distribution for a random variable

identify a binomial distribution and determine probability of
success, the mean, variance and standard deviation of a binomial
distribution.

Identify the normal distribution and its properties

Determine probabilities using the normal distribution

Analyze and determine probabilities for situations involving
contingency tables or cross-tabulation and probability trees

Use linear correlation and regression methods to analyze
relationships in bivariate data.
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Course Structure:
Mathematics 167 is divided into five units, which cover descriptive statistics,
probability, probability distributions and simple linear correlation and
regression.
Unit 1, “Introduction to Statistics,” is designed to introduce the field of statistics;
and present many of the terms used throughout this course.
Unit 2, “Collection and Organization of Data,” examines what a statistics
practitioner does with the vast quantity of numbers that form the raw data: how
he or she organizes it and presents it in tables and graphs.
Unit 3, “Descriptive Statistics,” examine how a statistics practitioner computes
various summary measures of location, variability and position.
Unit 4, “Introduction to Probability and Probability Distributions,” the material
in the two modules of this unit will help us determine the degree of certainty (or
uncertainty) with which we can make conclusions about a population, based on
observed sample results. The material studied in ‘Probability Distributions’
explores the concept of probability distributions including mean and variance,
and applies this concept to two commonly used probability distributions in
statistics: the binomial distribution and the normal distribution.
Unit 5, “Linear Correlation and Regression” focuses on the relationship between
two variables, using correlation analysis to determine the strength of the
relationship, and regression analysis to establish a mathematical formula for the
relationship.
Some units are divided into several modules, which involve readings from the
textbook, class notes and exercises and assignments designed to ensure that you
gain practice in the important statistical techniques. Each unit closes with a selftest designed to allow you to judge your mastery of the material. The self-tests
come with complete solutions.
After you have completed the unit self test, you are to complete the unit
assignment, a graded exercise. After you have successfully completed the first
three units of this course you will be ready to take the first course examination.
Once you have successfully completed unit four of this course, you will be
prepared to take the second course examination. Unit five will be tested as a part
of the final examination. Once you have successfully completed all five units of
this course you will be ready to write the final examination.
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Course outline: Topics/Objectives
Pre-unit Module
After completing the readings and exercises for this section, you should be able
to

Compute quantities and report results using rounding basics

Use sigma notation to perform summation

Graphing a straight line using different starting information
Unit 1: Introduction to Statistics
Module 1: Introduction to Statistics
After completing this module, you should be able to define and use in context

The term ‘statistics’ and why we need it

The nature of data and the types of data that can be collected

Descriptive and inferential statistics

Quantitative and qualitative, discrete and continuous variables

The categories of numerical data that are most relevant to statistical
analysis: nominal, ordinal, interval and ratio.
Module 2: Sampling
After completing this module, you should be able to define and use in context

Population, sample and census

Experimental and observational studies

Random sampling

Types of random sampling including simple random and systematic,

Types of biased sampling including convenience and haphazard
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
Sampling with and without replacement

Stratified random sampling with proportional allocation

Stratified sampling

Cluster sampling
Module 3: Questionnaire and Survey Design and Data Collection
After completing this module, you should be able to define and use in context

A glance at experiments and experimental design

Control and treatment groups

Collecting data

Experimental design and the survey

Rules for a well-designed survey

The questionnaire

Rules for the respondent-friendly questionnaire

Choosing a sample

Focus groups and pre-survey implementation tests
Unit 2: Collection and Organization of Data
Module 1: Measurements in Statistics
After completing the readings and exercises for this section, you should be able
to
1. define and use in context

Types of variables

Types of data

Levels of measurement
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
Errors: Random and Systematic

Compounding Errors

Accuracy and Precision
2. Compute

Absolute and Relative Errors

Percentage Points and Raw Percentage
Module 2: Organizing and Graphing Qualitative Data
After completing the readings and exercises for this section, you should be able
to

construct a frequency distribution that includes frequencies, relative
frequencies and percentage frequencies, given raw data for a qualitative
or categorical variable

construct a histograms

construct a bar graph and a pie chart

define a few cautions about graphical representations of data
Module 3: Organizing and Graphing Quantitative Data (Grouping Data)
After completing the readings and exercises for this section, you should be able
to

Construct stem-and-leaf displays and dotplots, and identify possible
outliers, given raw data.

Grouping terminology

Grouped data tables

Construct a frequency distribution that uses either a “less than” or not
“less than” method for writing the classes, given raw data for a
continuous variable.
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Note: This distribution will include class limits, class boundaries,
midpoints, frequencies, relative frequencies, percentage frequencies,
cumulative frequencies, and cumulative percentage frequencies.

construct the following graphs: histogram, relative frequency histogram,
frequency polygon, relative or percentage frequency polygon, ogive, and
relative or percentage ogive.

construct a frequency distribution using single-valued classes, given raw
data.

Note: This distribution will include frequencies, relative frequencies and
percentage frequencies.

construct a bar graph for the distribution described in Objective 3, above.

interpret frequencies, relative and percentage frequencies, cumulative
frequencies, cumulative relative frequencies and cumulative percentage
frequencies, given a frequency distribution or a related graph.

Distribution shapes

interpret symmetric, skewed and uniform distributions
Unit 3: Descriptive Statistics
Module 1: Central Tendency for Ungrouped Data
After completing the readings and exercises for this section, you should be able
to

compute the mean, median and mode, given ungrouped (raw) sample
data or ungrouped population data.

Selecting the appropriate measure of center.

Population means and sample means.
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
determine how the skewness of a data set affects the relationship between
the mean, median and mode.
Module 2: Dispersion (Variation) for Ungrouped Data
After completing the readings and exercises for this section, you should be able
to

compute the range, variance and standard deviation, given ungrouped
(raw) sample data or ungrouped population data.

identify the advantages and disadvantages of using the range and
standard deviation as a measure of dispersion for different types of data
sets.
Module 3: Mean, Variance and Standard Deviation for Grouped Data
After completing the readings and exercises for this section, you should be able
to

After completing the readings and exercises for this section, you should be
able to compute the mean, variance and standard deviation, given
grouped sample or grouped population data.
Module 4: Use of Standard Deviation
After completing the readings and exercises for this section, you should be able
to

use Chebyshev’s Theorem with any distribution to find the proportion or
percentage of the total observations that fall within a given interval about
the mean as an interpretation of the standard deviation.
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
use the Empirical Rule with any bell-shaped distribution to find the
proportion or percentage of the total observations that fall within a given
interval about the mean as an interpretation of the standard deviation.
Module 5: Measures of Position; Box Plots
After completing the readings and exercises for this section, you should be able
to

compute the three quartiles (Q1, Q2, Q3), the five-number summary, the
interquartile range, percentiles and percentile ranks, given ungrouped
(raw) sample data or ungrouped population data.

interpret the three quartiles (Q1, Q2, Q3), the interquartile range,
percentiles and percentile ranks in the context of a given problem.

construct a box-and-whisker plot, given ungrouped (raw) sample data or
ungrouped population data.

determine the three quartiles, the lower and upper inner fences, the
skewness, and outliers (if any), given a box-and-whisker plot.

Define, use in context and compute the z-score
Unit 4: Basic Probability and Probability Distributions
Module 1: Basic Probability: Experiments, Outcomes and Sample Spaces
After completing the readings and exercises for this section, you should be able
to

define, and use in context, the key terms:
experiment, outcome, sample space, simple and compound event

identify all possible outcomes of an experiment using a tree diagram, a
Venn diagram, or both.
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Module 2: Determining Probability:
After completing the readings and exercises for this section, you should be able
to

define, and use in context, the properties of probability.

probability

classical theoretical probability, relative frequency (experimental)
probability, and subjective probability

Law of Large Numbers

compute probabilities using the classical probability rules: the Addition
Rule and the Multiplication Rule.

Determining probabilities from a Contingency Table
Module 3: Random Variables and Probability Distributions:
After completing the readings and exercises for this section, you should be able
to

define, and use in context, the key terms: random variable, discrete
random variable and continuous random variable, probability distribution
of a discrete random variable.

construct a probability distribution in table or graph form, given a discrete
random variable defined for an experiment.

use a probability distribution to find the probabilities of various simple
and compound events.

define, and use in context, the key terms listed below.

mean of a discrete random variable

standard deviation of a discrete random variable

compute the mean and standard deviation of a discrete random variable.
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Module 4: the Binomial Distribution:
After completing the readings and exercises for this section, you should be able
to

define, and use in context, conditions of a binomial experiment, binomial
distribution

construct a binomial probability distribution, given a binomial
experiment.

compute probabilities associated with a binomial experiment, using the
binomial formula, a binomial table, or both.

compute the mean and standard deviation for a binomial distribution.
Module 5: the Normal Distribution:
After completing the readings and exercises for this section, you should be able
to

The normal distribution and its relative frequencies

The normal distribution and area under the curve

identify and use the three properties of a normal distribution:
the total area under the curve of a normal distribution is equal to 1.
the curve is symmetrical about the mean.
the tails of the curve extend indefinitely.

Define and use in context normally distributed variables and values

compute probabilities for a standard normal distribution.

compute probabilities for any normal distribution, given the mean and
standard deviation.

determine the z values (z-scores) and x values for a normal distribution,
when an area under the normal curve is known.
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
Simulate a normally distributed variable

Work with normally distributed variables using the 68-95-99.75 Rule

The Central Limit Theorem
Unit 5: Linear Correlation and Regression
Module 1: Linear Correlation
After completing the readings and exercises for this section, you should be able
to

define, and use in context, the key terms: linear correlation, positive,
negative, zero, perfect positive and perfect negative linear correlation.

Measure the strength of a correlation by computing the linear correlation
coefficient, given population or sample data.

demonstrate an understanding of the nature of the linear relation between
two variables by computing and interpreting the correlation coefficient
and the coefficient of determination,

Some difficulties associated with the interpretation of correlations

determine the least squares regression equation and interpreting the
coefficients a and b,

plot the scatter diagram and the regression line,

compute a point estimate of the dependent variable, given a value for the
independent variable.
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Student Evaluation
Your final grade in STAT 120 is based on the grades you achieve in two unit
assignments, two course examinations, a group research project and a final
examination.
NOTE: The assignments, each worth 5% of the final grade, are designed to
challenge you. They will contain only problems that you can solve using the
skills and knowledge you acquired while working through this course. Some of
the problems of the assignments will assigned directly from the text while others
will be assigned from more
The course exams are each worth 15% of the final grade and will cover material
presented in the five units of the course. The course exams will be a supervised
examination conducted in a manner consistent with college examination policy.
The examinations will consist of problems similar in nature to those presented in
the unit self-tests and the unit assignments.
For the group research project you will, working in a group or individually, pick
a topic for research then collect the data using a questionnaire that you will
design. After collecting the data you will use the methods of descriptive statistics
to organize the data, develop the pertinent distribution for the data and then
summarize the data with the various statistical measures. This project is worth
20% of the final grade.
The final examination is worth 40% of your final grade and is comprehensive. It
will be a supervised examination conducted in a manner consistent with college
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examination policy. The examinations will consist of problems similar in nature
to those presented in the unit self-tests and the unit assignments.
To pass this course, you must achieve a composite total of at least 60%.
The course is broken down into 3 assessments
Assessment 1:
Assignment 1: 5%
Course Examination 1: 15%
Assessment 2:
Assignment 2: 5%
Course Examination 2: 15%
Assessment 3:
Research Project: 20%
In the course exams and the final examination, you are allowed to bring in one
8½ × 11 inch summary sheet that can include anything that you feel may help you
successfully complete the examination. For example, the summary sheet might
contain formulas and worked examples. You can use both sides of the summary
sheet.
You may not bring any books or notes into the examination, other than the
summary sheet noted above.
For security reasons, the summary sheet used in each examination must be
handed in with your completed examination.
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You may also bring a scientific calculator to each examination. However, no
programmable calculators or computers may be brought into any of the
examinations. If you have a graphing calculator, make certain that the memory
has been cleared.
Attendance: Attendance will be recorded for each class meeting (lectures and
labs). Regular attendance is expected and a penalty for excessive absences will be
imposed. Absence from more than 10 percent of the scheduled class sessions,
whether excused or unexcused, is excessive and the instructor may choose to exact
a grade penalty for such absences. For this class, absence from more than 4 class
meetings will be considered excessive and a penalty will be imposed. For each
day in excess of 4 days missed, 1% will be deducted from the student’s final
course average percentage.
Tutorial Center: The Tutorial Center offers free tutoring center to all STAT 120
students. It is located in City Campus Room 303 and is staffed by mathematics
and statistics lecturers and lab assistants. The open hours for the Statistics Help
Lab will be posted early in the semester. A handout will be given to each student
that will delineate the particulars of the Tutorial Center.
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Frequently Asked Questions
Students must make arrangements with lecturer prior to absence in any of the
course examinations. With such arrangements student will be entitled to a
supplemental examination on the first day back to class. The same student will
not be allowed to write supplemental exams for the other course exam without
written documentation (medical).
Since the due date of assignment will be known well in advance, no late
assignments will be accepted.
CHALLENGE OPTION
The Math 167 course program has a challenge credit option. To prepare, you
simply have to know the course material well enough to feel comfortable in an
examination situation.
Student must write their challenge examination within one month of registering
in the course. They are allowed only one attempt to write the examination. If the
challenge exam is failed, it cannot be written again. An unwritten challenge exam
will not be reissued.
REGRADING
Under certain circumstances, you have the option to request a regarding of your
examination at no extra charge. A student who is dissatisfied with a grade must
contact the instructor to discuss the grade and material in question before
making an appeal. Such contact must be made within one month of receiving the
grade. Be advised that whatever grade you obtain from the regrade is your final
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grade, regardless of whether it is lower, the same, or higher than the one you
have already been given.
Resources
An Introduction to Elementary Statistics
http://www.yale.edu/ynhti/curriculum/units/1986/5/86.05.03.x.html#f
Research Methods
http://www.socialresearchmethods.net/kb/statcorr.htm
Elementary Statistics Tutorial Page
http://www.mail.pittstate.edu/~winters/tutorial/
Hyperstat Online
http://www.davidmlane.com/hyperstat/
R.Hernandez Pageout
http://hernandez.caribe.pageout.net
MyStatlab (information on this resource will be given on the first day of classes)
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Grading Scale:
% Percentage
Rubric standard
points earned
Final Letter
Grade
90 – 100
Excellent
A
85 – 89
Very good
B+
80 – 84
Good
B
75 – 79
Satisfactory
C+
70 – 74
Average
C
65 – 69
Below Average
D+
60 - 64
Bare Passing grade
D
< 60
Fail
F
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